Horizontal Line in bottom 50% of the screen (Macbook 2008 Late edition)

If the GPU is going bad, the only real option is a logic board replacement. The GPU is ball soldered on. Although if the line is due to the GPU die overheating, you might get a little more life by taking the heatsink off and replacing the thermal paste along with cleaning the dust out.

The screen isn't too bad to do, but it'll come down to getting a decent replacement. Don't try to get the LCD alone. Make sure it comes with the housing/webcam too.

I would also plug this up to an external display or TV if you can. If you see the line on the external display, the issue is with the GPU. If you don't see the line, the problem is with the MacBook screen.

With overheating, I'd say that a good clean with the fan and heatsink could help a lot. It shouldn't bee too difficult to get in and use some canned air on the fan blades (Do not let the air spin the fan) and blow out the heatsink fins.

That is most likely an issue with the LCD Panel as @Thatstud suggested. It is unlikely to be a GPU issue.

Use @DeathStalker13's suggestion to use an external display (make sure to enable mirroring though), or you can take a screenshot using macOS. View the screenshot, but make sure to move or scroll the picture up/down slightly so that the screenshot does not overlay the line itself. You want to view that section of the screenshot at another higher or lower location on the screen or by viewing the screenshot using another device.

That means the LCD Panel is most likely bad. If this is the Aluminum model, then it will likely require the replacement of the entire Display Assembly especially if it also has an aluminum display bezel.

It looks like the lcd is damaged. Try KTelectronics.us, they fix macbook and very good at it. I repaired with them before

Yes, you can connect and use an external display. You can use the "Display" System Preferences to configure how the external display will work with the built-in display. However, the laptop may not be able to work with some of the newer external displays.